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lower semicontinuous multifunctions; continuous embedding; compact embedding; continuous selector; extremal solution; relaxation theorem
In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the $C^1(T,R^N)$-norm in the set of solutions of the “convex” problem (relaxation theorem).
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